SOLUTION: A food store a 10-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $1.00 per pound, and raisins cost $1.00 per pound. The mixture calls for t
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Question 158765: A food store a 10-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $1.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $12.00. How much of each ingredient did the store use? Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=amount of peanuts
and y=amount of cashews
and z =amount of raisins
Now we are told that:
x+y+z=10--------------------------------eq1
we are also told that:
2y=x------------------------------------eq2
and
($ are understood)
1.5x+y+z=12-----------------------------eq3
subtract eq1 from eq3 and we get
0.5x=2 divide each side by 0.5
x=4 lb----------------------------------amount of peanuts used
substitute x=4 into eq2 and we get:
2y=4 divide each side by 2
y=2 lb------------------------------------------amount of cashews used
substitute x=4 and y=2 into eq1 and we get
4+2+z=10 or
6+z=10 subtract 6 from each side
6-6+z=10-6
z=4 lb--------------------------------------------amount of raisins used
CK
4+2+4=10
10=10
and
(1.5)*4+2+4=12
6+2+4=12
12=12
Hope this helps---ptaylor
